Brain mapping studies are concerned with localization and evaluation of structural changes caused by various developmental or even disease processes. Cortical morphometry is a branch of brain mapping that studies changes in morphology on the periphery of the cerebrum. There are several approaches for achieving this goal. Most of these approaches [1
] start with a geometrical representation for the cortical surface, and establish a dense correspondence of homologous regions and points across a group of subjects. This correspondence is further used to drive the construction of a population-based atlas that maps all the subjects in a common reference frame. Accurate registration methods allow the reconciliation of various brain measures and enable consistent inter-subject comparisons both within and across different populations.
In this paper we follow a different approach. Instead of focusing on local geometric changes, and spatial registration, we attempt to represent and analyze global structural patterns on the cortex via continuous density functions that capture the variation of different cortical valued features. Our goal here is not to achieve a precise localized map of brain changes, but rather discover a set of pertinent global features that attempt to model the overall structural patterns. Lately, there is an emerging interest in understanding the underlying low dimensional structure at a population level [3
]. This idea is also exploited in Dalal et al. [6
], who propose a shape-based approach for cortical similarity. We are interested in extracting functions of cortical features that serve as compact representations of the underlying brain populations. In this paper, we focus on the cortex, and its regional segmentations in particular, and represent different parcellations using distributions of their features. These distributions at a cortical level, implicitly capture the global location of the feature, and at a regional level capture the underlying trend of the feature valued data. Additionally we use the Jensen-Shannon (JS) divergence [7
] for discriminating between the feature functions. There are several advantages to the proposed approach. i) The distribution functions are invariant to brain scale, translation, and orientation, ii) they are easily and efficiently computable, and iii) finally this approach does not require pairwise registrations, and hence can be effectively applied to sizable populations. The rest of the paper is organized as follows. We introduce the feature function representation in Sec. 2.1, and present the cortical matching approach in Sec. 2.2. Section 3 presents applications of this method to clustering, classification, and dimension reduction on a population from the ADNI dataset [8
], followed by discussion and conclusion.